Network management based on assessment of topological robustness and criticality of assets

ABSTRACT

A system and method of managing a network that includes assets are described. The method includes modeling the network as a directed graph with each of the assets represented as a node and determining alternative paths to each node from each available corresponding source of the node. The method also includes computing upstream robustness of each node, computing upstream robustness of the network, and computing downstream criticality of each node. Managing the network and each asset of the network is based on the upstream robustness and the downstream criticality of each node.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. application Ser. No. 16/000,818, filed Jun. 5, 2018 and entitled “Network Management Based on Assessment of Topological Robustness and Criticality of Assets,” which is a continuation of U.S. patent application Ser. No. 14/745,775, filed Jun. 22, 2015 and entitled “Network Management Based on Assessment of Topological Robustness and Criticality of Assets,” now U.S. Pat. No. 9,992,069, which is a continuation of U.S. patent application Ser. No. 14/665,398 filed Mar. 23, 2015 and entitled “Network Management Based on Assessment of Topological Robustness and Criticality of Assets,” now U.S. Pat. No. 9,923,778, which are hereby incorporated by reference herein.

BACKGROUND

The present invention relates to network management, and more specifically, to network management based on assessment of the topological robustness and criticality of assets.

There are many types of networks that include a number of assets that affect each other. Exemplary networks with a number of interdependent assets include a power network (power grid), gas network, and a water network. Reliability of such networks can depend not only on the assets themselves and their failure rates but also on the robustness of the network topology. Assets of a given network can be of different types and can be for different uses. For example, a power network includes electrical assets (e.g., transformers, switches, fuses) and non-electrical assets (e.g., support structures, poles).

SUMMARY

According to one embodiment of the present invention, a method of managing a network that includes assets includes modeling, using a processor, the network as a directed graph with each of the assets represented as a node; determining, using the processor, alternative paths to each node from each available corresponding source of the node; computing upstream robustness of each node; computing upstream robustness of the network; computing downstream criticality of each node; and managing the network and each asset of the network based on the upstream robustness and the downstream criticality of each node.

According to another embodiment, a network management system to manage assets of the network includes a memory device configured to store instructions, and a processor configured to process the instructions to compute upstream robustness of each node, compute upstream robustness of the network, compute downstream criticality of each node, and to manage the network based on the upstream robustness and the downstream criticality of each node.

According to yet another embodiment, a computer program product includes a tangible storage medium readable by a processing circuit and storing instructions for execution by the processing circuit to perform a method of managing a network that includes assets. The method includes modeling the network as a directed graph with each of the assets represented as a node; determining alternative paths to each node from each available corresponding source of the node; computing upstream robustness of each node; computing upstream robustness of the network; computing downstream criticality of each node; and managing the network and each asset of the network based on the upstream robustness and the downstream criticality of each node.

Additional features and advantages are realized through the techniques of the present invention. Other embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed invention. For a better understanding of the invention with the advantages and the features, refer to the description and to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the claims at the conclusion of the specification. The forgoing and other features, and advantages of the invention are apparent from the following detailed description taken in conjunction with the accompanying drawings in which:

FIG. 1 is a process flow of a method of managing a network based on determining upstream robustness and downstream criticality according to embodiments;

FIG. 2 is an exemplary graph used to identify nodes and connections for embodiments of the invention;

FIG. 3 shows the processes involved in computing upstream robustness at block 130 (FIG. 1 ) according to an embodiment; and

FIG. 4 is a block diagram of a processing system to implement embodiments of the invention.

DETAILED DESCRIPTION

As noted above, topological robustness can affect network reliability in addition to failure rate of assets within the network. Topological robustness of the network refers to whether multiple sources are available to a given asset such that, if one fails, the other(s) can continue to supply the asset, for example. A lack of robustness increases criticality of an asset. That is, for example, the only asset supplying several downstream assets is more critical than one of several assets supplying a downstream asset. The interplay between robustness and criticality, therefore, effects the management of the network. A less robust and more critical asset may require more frequent inspection, for example. Embodiments of the methods and systems described herein relate to determining upstream robustness as well as downstream criticality in order to manage the network and its assets. While an electrical network (grid) is discussed for exemplary purposes, the description herein applies to any network with interdependent assets.

FIG. 1 is a process flow of a method of managing a network based on determining upstream robustness and downstream criticality according to embodiments detailed below. Throughout the discussion herein, asset and node are used interchangeably because the representation of the assets in a directed graph is as nodes. At block 110, modeling the network as a directed graph includes indicating the assets of the network as nodes and showing the interconnection among the nodes as edges or paths which are further detailed below. Determining alternative paths to each target node from available sources, at block 120, leads to computing the upstream robustness of each target node at block 130. At block 140, upstream robustness of the network is computed. At block 140, an additional set of key performance indicators (KPIs) used for robustness assessment are also computed. At block 150, computing downstream criticality for each target node is performed along with computing an additional set of KIs for assessment of asset criticality. Managing the network at block 160 involves examining the robustness and criticality determined at the previous processes. Each of these processes is further detailed below.

FIG. 2 is an exemplary graph 200 used to identify nodes 210 and connections 220 for embodiments of the invention. Several nodes 210 are shown with connections 220 indicating the physical topology of the network. Steps involved in the generation of the graph 200 are known and are not detailed here. Generally, the physical topology is converted into a list of edges. Each edge is an ordered pair of two assets, and it is assumed that electric power flows between the pair of assets. The assets are represented by the nodes 210 and the connectivity 220 is defined by the edges. The nodes 210 may be classified in one of three categories: source assets that serve as the source of all electrical power in the grid, auxiliary assets (e.g., cables, poles, switches, protection devices) that are critical to delivery of electrical power to sink assets, and the sink assets that directly serve customers. In the exemplary graph 200, the nodes 210 include a source asset—source pp—a sink asset—endpoint s2—and auxiliary assets—cables c1-c6, transformers t1-t3, and open point o1. While the exemplary graph 200 pertains to a power network (grid), the embodiments detailed herein are not limited to a power network, as noted above.

Determining the set of alternate paths (at block 120) Pt from the source nodes to each of the target nodes t includes using a breadth-first search (BES). The BFS involves traversing the graph (e.g., 200 in FIG. 2 ) by beginning with the source node (e.g., pp in FIG. 2 ) and progressing through the nodes (210, FIG. 2 ) one-at-a-time from the root to its neighbors. The set Pt is given by: P_(t)={P_(t,1), P_(t,2), . . . , P_(t,m)}  [EQ. 1] The number of paths to the target node t is m. For the i^(th) path in the set Pt, which represents a length of l (l number of assets) from the source asset to the target node t, P_(t,i)={a₁, a₂, . . . , a_(l)}  [EQ. 2] Each element in the Pt set represents a path Pt,i, and each path Pt,i includes a set of intervening assets.

FIG. 3 shows the processes involved in computing upstream robustness at block 130 (FIG. 1 ) according to an embodiment. Generally, the processes include computing inter-path independency of each alternative path Pt,i in Pt 305, computing intra-path independency of the target node t in each alternative path Pt,i, in Pt 345, and computing the upstream robustness for each target node t based on the inter-path independency and the intra-path independency 370. Each of these processes if further detailed herein. At block 310, computing the universe Ut of assets between the target node t and the sources is as follow: U_(t)={P_(t,1)∪P_(t,2)∪ . . .520 P_(t,m)}  [EQ. ] Ut is the union of the paths in the set Pt. Determining the frequency of occurrences fc of each asset tin Ut, at block 320, is given by:

$\begin{matrix} {f_{c} = \begin{Bmatrix} {{f_{c} + 1},{{ifc} \in P_{t,i}}} \\ {f_{c},{{ifc} \notin P_{t,i}}} \end{Bmatrix}} & \left\lbrack {{EQ}.4} \right\rbrack \end{matrix}$ Computing the score sc of each component tin Ut is based on the score being an inverse of the frequency:

$\begin{matrix} {s_{c} = \frac{1}{f_{c}}} & \left\{ {{EQ}.5} \right\rbrack \end{matrix}$ Then, at block 340, computing the inter-path independency of a path Pt,i is based on summing the score of each component in the path and normalizing with the length of t path Lt,i:

$\begin{matrix} {{PI}_{t,i}^{inter} = {\frac{1}{L_{t,i}}{\sum\limits_{i \in P_{t,i}}s_{i}}}} & \left\lbrack {{EQ}.6} \right\rbrack \end{matrix}$

At block 350, determining the length of the path Pt,i in terms of the number of components in the path is based on the cardinality (number of elements) of the path (set) Pt,i and is given by: L_(t,i)=|P_(t,i)|  [EQ. 7] Then, at block 360, computing the intra-path independency of a target node t in a path Pt,i is as a function of the length of the path determined from EQ. 7.

$\begin{matrix} {{PI}_{t,i}^{intra} = \frac{1}{L_{t,i} + 1}} & \left\lbrack {{EQ}.8} \right\rbrack \end{matrix}$ The “+1” in the denominator is included to include the target node t, because the target node t may fail, as well. Once the inter-path independency (at block 340, based on blocks 310-340) and the intra-path independency (at block 360, based on blocks 350 and 360) are computed, upstream robustness of the target node t is computed, at block 370, as:

$\begin{matrix} {R_{ups}^{t} = {\sum\limits_{i = 1}^{m}{{PI}_{t,i}^{inter}{PI}_{t,i}^{intra}}}} & \left\lbrack {{EQ}.9} \right\rbrack \end{matrix}$ The number of alternative paths to the target node t is m. As EQ. 9 indicates, the upstream robustness is a function of the level of disjointedness between all alternative paths to the target node t (represented by the inter-path independency) and the number of components on which the target node t depends to reach a source in each of these paths (represented by intra-path independency). That is, the more disjointed the alternative paths are (such that a failure in one is less likely to affect another) and the fewer components between the target node t and each source of each path (such that there are fewer chances of the path to the source being disrupted), the more robust the target node t is.

At block 140 (FIG. 1 ), computing upstream robustness of the network G is based on the upstream vulnerability of individual assets of the network G. For the network G with N assets (N target nodes in turn), the network upstream robustness is given by:

$\begin{matrix} {R_{ups}^{G} = {\sum\limits_{i = 1}^{N}R_{ups}^{i}}} & \left\lbrack {{EQ}.10} \right\rbrack \end{matrix}$ The network upstream robustness measures the aptitude of the network to continue operation (e.g., deliver electric power to nodes of the network in the exemplary case of an electrical grid application). Thus, only the robustness of each asset is considered in computing the network robustness. Additional KPIs are also computed at block 140. The path count (PCt) of a target node t assesses the topological redundancy in reaching the target node t from available sources. The path count evaluates the total number of alternative paths to the target node t from the source(s) and is computed as the cardinality of Pt (determined in EQ. 1) as: PC_(t)=|P_(t)|  [EQ. 11] The effective disjoint path count (EDPCt) of a target node t quantifies the effective number of independent paths from a source to the target node t. The EDPCt accounts for the disjointedness of each path Pt,i (from EQ. 2) in the set of paths Pt and is computed as a summation of the inter-path independency of each path from a source to the target node t:

$\begin{matrix} {{EDPC}_{t} = {\sum\limits_{i = 1}^{m}{PI}_{t,i}^{inter}}} & \left\lbrack {{EQ}.12} \right\rbrack \end{matrix}$ The effective path length (EPLt) of a target node t gives the average effective distance to sources of the target node t in terms of the number of intervening assets. The EPLt is computed as a number of assets per effective disjoint path between the target node t and its sources:

$\begin{matrix} {{EPL}_{t} = \frac{❘U_{t}❘}{{EPDC}_{t}}} & \left\lbrack {{EQ}.13} \right\rbrack \end{matrix}$

At block 150 (FIG. 1 ), downstream criticality is computed for each target node t. Because, with respect to activity downstream of a given asset, the asset is not a target (as it is for an upstream source), the term component c is used rather than target node t. To determine the downstream criticality of a component c of a network G, the component c is removed from the network to obtain a reduced network G′: G′=G\c   [EQ. 14] The network upstream robustness is computed for G′, the reduced network, based on the processing detailed above at blocks 110 through 140. Then, the downstream, criticality of the component c is computed as a drop in the network upstream robustness of the network G (see EQ. 10):

$\begin{matrix} {C_{down}^{c} = {\frac{\left( {R_{ups}^{G} - R_{ups}^{c}} \right) - R_{ups}^{G^{\prime}}}{\left( {R_{ups}^{G} - R_{ups}^{c}} \right)}*100}} & \left\lbrack {{EQ}.15} \right\rbrack \end{matrix}$ The use of the robustness of the component c in both the numerator and denominator acts as a correction factor to ensure that the downstream criticality of a leaf node is 0. A leaf node is one with no children such that it has no effect on assets downstream of itself Additional KPIs are also computed at block 150. The disconnection impact index (DIIt) of an asset t quantifies the impact of its removal from the network from different perspectives. Consequences of the removal of an asset t can be measured based on different aspects (consequences of the removal) including, for example, the number of disconnected assets, the number of disconnected customers (from, the network), the amount of lost demand, and the amount of lost revenue. Consequences represent the set of these and other consequences, and s_(t)={a₁, a₂, . . . a_(l)}  [EQ. 16] EQ. 16 indicates the set of assets that are disconnected upon removal of the asset t. Then DIIt is given by:

$\begin{matrix} {{DII}_{t} = {\sum\limits_{t \in s_{t}}{consequences}_{t}}} & \left\lbrack {{EQ}.17} \right\rbrack \end{matrix}$ With regard to the consequences, for example, quantifying DIIt of an asset t in terms of the number of disconnected customers requires evaluating the summation of the number of disconnected customers per disconnected asset in the set of assets shown in EQ. 16.

Determining the upstream robustness and downstream criticality of the assets of the network, as well as the network as a whole facilitates managing the network at block 160. The relative criticality of a given asset may suggest a more or less frequent inspection and maintenance period, for example. More critical assets may be inspected and maintained more often than less critical assets. As another example, the source of a less robust asset may be maintained more often than the source of a more robust asset. The information may be used to upgrade the system, as well. For example, a redundant source may be added for highly critical assets.

FIG. 4 is a processing system 400 configured to implement embodiments described herein. The processes detailed herein may be implemented by one or more processors (processing circuits) 410 based on instructions stored in one or more memory devices 420. The memory devices 420 may additionally store data used in the processing. The instructions and one or more memory devices 420 represent a computer program product to implement the detailed processes. The processing system 400 may additionally include an input interface 430 (e.g., keyboard, wired or wireless communication link) to receive commands or data, as well as an output interface 440 (e.g., display device, communication link) to send output. The computer program product (420) and processor 410 may be stand-alone components or may be integrated with other components of the network.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one more other features, integers, steps, operations, element components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated

The flow diagrams depicted herein are just one example. There may be many variations to this diagram or the steps (or operations) described therein without departing from the spirit of the invention. For instance, the steps may be performed in a differing order or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention.

While the preferred embodiment to the invention had been described, it will be understood that those skilled in the art, both now and in the future, may make various improvements and enhancements which fall within the scope of the claims which follow. These claims should be construed to maintain the proper protection for the invention first described.

The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein, was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein. 

What is claimed is:
 1. A network management system to manage assets of the network, the network management system comprising: a processor; and a memory storing instructions for execution by the processor to perform a method of managing the network, the method comprising: determining a set of paths of the network between each of a set of nodes of the network; determining an upstream robustness of each node of the set of nodes based on an inter-path dependency of each path of the set of paths, the upstream robustness of a particular node being based on a number of paths from different nodes to the particular node; determining an upstream robustness of the network based on the upstream robustness of each node of the network; determining downstream criticality for each node of the set of nodes of the network by: removing that particular node of the network to obtain a modified network; determining an upstream robustness of the modified network without that particular node; and determining a downstream criticality for the particular node based on the upstream robustness of the modified network; and managing the network based on the upstream robustness of each node and the downstream criticality of each node, managing the network includes modifying a schedule for inspection of assets of the network.
 2. The network management system of claim 1, wherein the determining an upstream robustness of each node of the set of nodes includes determining an intra-path of each path of the set of paths.
 3. The network management system of claim 2, wherein the intra-path of each path is based on a length of each path.
 4. The network management system of claim 1, wherein the inter-path dependency of each path of the set of paths is based on an effected disjoint path count.
 5. The network management system of claim 1, the method further comprising determining an average effective distance from the set of nodes in each path in the set of paths.
 6. The network management system of claim 1, wherein the managing the network includes increasing inspection frequency of an asset corresponding to a first node when the first node has a lower upstream robustness than a second node or a higher down-stream criticality than a third node.
 7. The network management system of claim 1, wherein the network is an electrical power network, and an edge between a pair of the nodes represents a flow of electric power between a pair of assets corresponding to the pair of nodes.
 8. The network management system of claim 1, wherein the network is a gas network.
 9. The network management system of claim 1, wherein the network is a water network.
 10. The network management system of claim 1, wherein the upstream robustness of each node is inversely proportional to a number of nodes between each node of the set of nodes.
 11. The network management system of claim 1, wherein the determining the downstream criticality for the particular node is further based on a number of disconnected customers in the modified network.
 12. A method comprising: determining a set of paths of a network between each of a set of nodes of the network; determining an upstream robustness of each node of the set of nodes based on an inter-path dependency of each path of the set of paths; determining an upstream robustness of the network based on the upstream robustness of each node of the network; determining downstream criticality for each node of the set of nodes of the network by: removing that particular node of the network to obtain a modified network; determine an upstream robustness of the modified network without that particular node; and determining a downstream criticality for the particular node based on the upstream robustness of the modified network; and managing the network based on the upstream robustness of each node and the downstream criticality of each node, managing the network includes modifying a schedule for inspection of assets of the network.
 13. The method of claim 12, wherein the determining an upstream robustness of each node of the set of nodes includes determining an intra-path of each path of the set of paths.
 14. The method of claim 13, wherein the intra-path of each path is based on a length of each path.
 15. The method of claim 12, wherein the inter-path dependency of each path of the set of paths is based on an effected disjoint path count.
 16. The method of claim 12, the method further comprising determining an average effective distance from the set of nodes in each path in the set of paths.
 17. The method of claim 12, wherein the managing the network includes increasing inspection frequency of an asset corresponding to a first node when the first node has a lower upstream robustness than a second node or a higher down-stream criticality than a third node.
 18. The method of claim 12, wherein the upstream robustness of each node is inversely proportional to a number of nodes between each node of the set of nodes.
 19. The method of claim 12, wherein the determining the downstream criticality for the particular node is further based on a number of disconnected customers in the modified network.
 20. A computer program product comprising: a non-transitory storage medium readable by a processing circuit and storing instructions for execution by the processing circuit to perform a method of managing a network that includes assets, the method comprising: determining a set of paths of a network between each of a set of nodes of the network; determining an upstream robustness of each node of the set of nodes based on an inter-path dependency of each path of the set of paths; determining an upstream robustness of the network based on the upstream robustness of each node of the network; determining downstream criticality for each node of the set of nodes of the network by: removing that particular node of the network to obtain a modified network; determine an upstream robustness of the modified network without that particular node; and determining a downstream criticality for the particular node based on the upstream robustness of the modified network; and managing the network based on the upstream robustness of each node and the downstream criticality of each node, managing the network includes modifying a schedule for inspection of assets of the network. 